One way to solve this problem is to "guess" a solution. Since the form of your equation is very basic, this guess is usually taught as a standard method.

As your solution suggests, your guess should be the following:
[tex]f(\phi)=e^{r\phi}[/tex]
Simply replace every function f with that equation above and solve for the unknown, r. Then, once you find r, plug it back into the equation above. Note that the "A" in your answer is an arbitrary constant used to solve with initial conditions.

thanks - knew it was something simple. I actually remembered the other approach too, where you replace f'' with r^2, f' with r, and f with 1, and then solve for what r is. But either approach gives the same result.